In a large bowl, mix together 1 1/4 cups of the water, all-purpose flour, whole wheat flour, sourdough starter, and salt. Cover loosely with plastic and allow to ferment at room temperature overnight, 10 to 12 hours.
In the morning, mash the banana in a small bowl. Add the banana, coconut milk, remaining 1/4 cup water, baking powder, and baking soda to the fermented flour mixture in the large bowl. Stir vigorously with two chopsticks to break up the thicker fermented mixture, continuing until well blended. It's fine if the batter is still slightly lumpy.
Allow the batter to sit for 15 minutes. Preheat the waffle iron for 3 to 5 minutes, according to the manufacturer's directions, while the batter is standing.
Spray both grids of the waffle iron generously with oil. Pour or ladle the batter into the center of the iron, covering no more than two-thirds of the iron’s surface for the first waffle. Adjust the amount as needed for subsequent waffles. Bake each waffle for 3 to 5 minutes, or until it can be removed easily. Re-spray the grids generously with oil prior to each waffle.